Question

Is heat a parabolic equation?

Answer 1

1. The heat equation is a parabolic equation.
2. The heat equation is the prototypical example of a parabolic partial differential equation.
3. A partial differential equation is what the heat equation is. The solutions to the heat equation are sometimes referred to as caloric functions.
4. The heat equation, the classic parabolic partial differential equation, is one of the most commonly studied problems in pure mathematics, and its analysis is considered fundamental to the broader field of partial differential equations.
5. The heat equation is written as:
6. $\frac{\partial u}{\partial t}=∆u$
7. It's an example of a partial differential equation with a parabolic form.

Hence, heat is a parabolic equation.